Existence and uniqueness of weak solutions to quasilinear PDEs with critical data

TL;DR

This paper proves the existence and uniqueness of bounded weak solutions for certain quasilinear PDEs with various initial data conditions.

Contribution

It introduces new results on the existence and uniqueness of solutions under less restrictive initial data assumptions.

Findings

Proves global existence and uniqueness for bounded, uniformly continuous initial data.

Establishes existence of solutions with merely bounded initial data.

Analyzes properties of the solutions obtained.

Abstract

We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when the initial data is merely bounded.